<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-09-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001207074</issuerCik>
        <issuerName>VIRTUSA CORP</issuerName>
        <issuerTradingSymbol>VRTU</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001449543</rptOwnerCik>
            <rptOwnerName>Kalia Ranjan</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 2000 WEST PARK DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WESTBOROUGH</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01581</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP &amp; Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>common stock</value>
            </securityTitle>
            <transactionDate>
                <value>2012-09-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>925</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.3401</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>97377</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The sale of vested restricted stock was executed in multiple trades at prices ranging from $17.26 to $17.39 per share. The price reported above reflects the weighted average sale price. The reporting person hereby undertakes to provide upon request to the SEC staff, the issuer or a security holder of the issuer full information regarding the number of shares and prices at which the transaction was effected.</footnote>
        <footnote id="F2">Includes 2,500 shares of performance based restricted stock granted under the Company's 2007 Plan in 11/08, which vest only upon the Company's achievement of certain revenue and operating income targets for the fiscal year ending March 31, 2013. Includes 5,000 shares of performance based restricted stock under the Company's 2007 Plan on August 2, 2012, which vest only upon the Company's achievement of certain revenue targets for the fiscal year ending March 31, 2013. The grantee retains voting rights with respect to restricted shares unless and to the extent that such shares do not vest and are forfeited.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Paul D. Tutun, Attorney in Fact</signatureName>
        <signatureDate>2012-09-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
